I'm a mathematical physicist who likes explaining stuff. I'm the Maxwell Fellow of Public Engagement at the School of Mathematics and the School of Physics and Astronomy at the University of Edinburgh.
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2026-04-01T17:51:18Z Event JSON
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Last Notes npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Kings Day shows yet again that the least powerful Americans are the most courageous. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…j9f5 - the Choctaw don't own most of the land over which they have jurisdiction, and I can't quickly find out how much land they do own. So far they seem to be doing solar on a smaller scale: npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez As confirmed by a 2020 Supreme Court decision, 15% of Oklahoma is under jurisdiction of the Choctaw Nation. Now the Choctaw have used their power to prevent ICE from getting a big detention center! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez The proton, 1836 times heavier than the electron, is made of two up quarks and a down, with two of their spins aligned and one pointing the other way. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez The arXiv is separating from Cornell University, and is hiring a CEO, who will be paid roughly $300,000/year:[email protected] . The salary is expected to be around $300,000, though the actual salary offered may differ. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Beato isn't really saying AI will fail: despite the denialists who claim it's never good for anything, it's too useful for too many things to simply "fail". He's claiming something more interesting: for many purposes, big AI can be replaced by LLMs that you can run on your laptop. They already exist and you can download them for free. So the massive investment in data centers, expecting huge profits when we all start paying monthly fees to run LLMs, may soon be undercut by something cheaper. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Manet's famous painting Un Bar aux Folies-Bergère never appealed to me. But now I realize its genius, and my spine tingles every time I see it. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Another place I want to visit on my trip to New Mexico is called Aztec Ruins - named that before white folks realized the ancestral Puebloans were a very different civilization. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Have you read There Is No Antimemetics Division? Would I like it? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez In the northern hemisphere, the sun moves clockwise in the sky. This is why clocks, which were based on sundials, have hands that move clockwise. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…gvxt - I don't know what "sort the partials out to see what it looks like without them" means. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…gvxt @nprofile…920r - yes, you can call some of them overtones. But I'm not sure that's the full explanation of the pattern we're seeing here! It should be related to the continued fraction expansion of ln(3)/ln(5) - or in other words, which powers of 3 are close to powers of 5. I showed that's part of the story. But I don't know the full story. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez So far I've been trying to understand the complicated waves in the function npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez To get a better picture of the *slow* oscillations in npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez There are fascinating connections between the Riemann zeta function and music theory. I'll probably write a paper about this, but I can't resist talking about a little piece of the story. I will *not* explain what this has to do with music, since I want to tell that exciting story later on, and do a really good job of it. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…h6a3 - thanks, I'll check out this show in preparation for my own pilgrimage! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…8qh7 @nprofile…xdkd - I used to read Gene Ward Smith on sci.math and such, but I never paid much attention to his tuning theory stuff. I feel terribly sorry that I didn't, since he died of COVID in 2021: npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez My god! What an amazing blog article! For the last few weeks I've been studying the work of Gene Ward Smith, who discovered a connection between muic theory and the Riemann zeta function. But it turns out @nprofile…xdkd has been thinking abou this for years... and what she has discovered is much richer and more beautiful than I had imagined. This changes everything! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…uk82 - oh! I'm starting to read about this, and so far it seems like there were extensive trading networks in the Americas. I haven't read about anything particularly linking Puebloans to Mayans genetically. But I'll keep reading. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…ygne - was it easy to find everything when you got there? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…uk82 - scarlet macaws in New Mexico? Or cacao? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…f5pz - oh, interesting! I didn't know that about the thick-billed parrots. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…ju9m - this is amazing! Or rather: many of us don't learn enough about this in school, so we tend to underestimate these people. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…a638 - sounds cool. I went to White Sands once, but have no clear picture of what's between that and Chaco Canyon. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…8qh7 - the use of honey suggests they weren't insane. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…l7vu - thanks, that was a great listen. I'm planning to do a lot of study before visiting various sites this spring. This video was a good springboard toward digging deeper into these matters, because it situated Chaco in an interacting network of different cultures. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…t5a9 - I said it would be fun, but I don't know if I'll ever do it: I have too many project half-finished. Right now my main passion is the mathematics of tuning systems. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…t5a9 - Does a typical good, meaty first course on algebraic geometry give some intuition for the bigrading on the cohomology of a smooth complex variety? I don't know. I never took such a course, but I think there are lots of ways such a course could go. This stuff is in Griffiths and Harris, but that book says a lot more about complex manifolds than some intros to algebraic geometry. (That's why I like it: I'm really more of an analyst.) npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…xuq7 - I think that first section was really just a rapid attempt to convince people that there's more to algebraic geometry than a pile of slick abstract definitions. It may have scared as many students as it intrigued. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…rgsr - I didn't actually ever sleep through a class. I just never took a course on commutative algebra. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…xuq7 - nice! It looks like a rocket-fuel-propelled approach to algebraic geometry where he talks about zeta functions and cohomology theories on page 3 and then gets serious. 😆 npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…xuq7 - Oh great! I haven't ever looked at a book by Raskin, in fact I don't even know the name Raskin. But I've been thinking there should be an approach to algebraic geometry that goes like this. I only heard about this approach long after I suffered through the Hartshorne approach (listening to people talk about it, not actually studying it very hard). npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…a3ey - it's a great read, though not all at once. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…jrcx - it looks like an error-ridden text. Throw it out and get a better book on number theory! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…0g3j - you can change the conclusion, right? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…sz8l @nprofile…u3x7 - It's pretty obvious that having Terry Tao use their software is better than any advertisement that money could buy. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…az9a - I was explaining the situation to my followers around the world, many of whom don't know the intricacies of the US federal system. I don't think Trump cares about laws and the constitution, but there's a whole network of people who do care, so when he breaks the laws they get energized to push back, and this does have an effect. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…ezv6 - there's no link there. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…az9a - it would be illegal, indeed against the US Constitution, for Trump to attempt to take over the election process. In fact I recently added a remark about this to my original post, for people unfamiliar with the US system. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…5ahq - I'll check it out. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…5ahq - I'd never say radically improved democracy is impossible. We need not only an appealing new system, but a way to get there from here. I hope you've written, or will write, a detailed tactical manual on how to get there from here. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…5ahq - Lots of people are discussing those questions. But it's also important to avoid falling off the cliff right now. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…9fju - sure thing! I've never been to the Calumet region. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…3vpz - interesting enough. A bit more color variation on short distance scales might make the landscapes more realistic, especially the one at lower right which has large regions of dark orange (cloud shadows?). The clouds are simple blobs. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…lfhd @nprofile…t6k2 - I read the vaguely similar one Trading Places, about a British and a California professor who trade places. Fun study of stereotypes, probably dated now. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…fh5j - oh well! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…t6k2 @nprofile…z2n3 @nprofile…s7d2 - just to be clear, where @nprofile…z2n3 quoted me as writing ω2 and ωω, I actually wrote ω^2 (ω squared) and ω^ω (ω to the ω). I was trying to say that PRA is powerful enough to prove that the Ackermann function is total because it can handle recurious up to ω^ω, but proving the Ackermann function is total only requires recursion up to ω^2. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…r9vg - I guess they'll have to see by talking to each other! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…zyzh - I even heard that some people listed their MathOverflow (or was it StackOverflow) reputation scores on their CVs. Blech. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…zyzh - nothing in MathOverflow says a question has a single answer. Many questions there have lots. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…wncd - great! I have been very busy and distracted but I ***do*** want to return to this project and finish it off. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g0zc - Interesting! So if you say a young man is luckless and feckless, that's a nice euphemism for something that rhymes. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g0zc - opposite of feckless? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g0zc - the shepherd's pie is f***ing good! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…4qpt - the symmetry brings out the beauty. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…jrcx - @nprofile…t6k2 would have opinions on this, though he may be tired of talking about it. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…j4wh - really??? Can't AI solve that problem? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…a3ey - noble of you! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…a3ey - I too promise to no longer publish more than 7 papers per year. 😆 npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…2sx2 - they've got lots of nice posts here. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…2sx2 - there are some very nice experts on constructive mathematics here on Mathstodon, e.g. @nprofile…t6k2 and @nprofile…ldyp. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…e2fl - now I get to check out #SolarPunkSunday! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…6fwm - what a great story! I could enjoy a whole novel about beavers on the San Pedro, written in a similar style, with maps. But I'll be frequenting your blog now, for other tales. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…nekg - that would definitely be disturbing if I were out camping. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…80ng - will do! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…ccq6 - indeed, that's how I often feel these days. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…x8fk - we see animals called bobcats in our back yard in Southern California, but these are actually lynxes... so I'm a big fan of the lynx. Hurrah for the Iberian lynx! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…659g - is that on the California coast south of Big Sur? That's where I've seen such rocks. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…r0xq - I'm afraid so! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…qlgd - Was Lior Pachter a grad student at UCR for a while? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…t6k2 - I don't even know who is to blame for the website, the Times Higher Education folks or Elsevier. It claims to list 750 schools in order but I only see 4. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…llgf - I did my PhD at MIT, where I took a course on continental philosophy in the math department. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…zjjl - string theory has never left. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…0htv - yes, I think that's the one. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…sz8l - for decades string theory has been stuck on the problem of getting the cosmological constant to come out with the right sign. This is one of several big problems with the theory. So I can see why string theorists would be excited, even though it's working in the wrong dimension and the cosmological constant 'decays'. The rest of us should take a wait and see attitude. The Quanta headline is hyping this development; the article itself is better. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…wu7v - in our universe there are 4 dimensions counting time. In this version of string theory there are 5 dimensions counting time. It doesn't describe our universe. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g3ts - I'm not particularly eager to answer questions about entanglement, since my course is about the Standard Model and the physics and math needed to understand that. On the other hand, I'm extremely eager to get questions on my YouTube videos that are about what I'm trying to explain. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…j6ga - but not before that. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…gu9p - I'll think about that! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…tj4e - Great show! But if you get anywhere near Jessica Fletcher watch out: your life is in danger. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…mgke - Thanks! I responded in a bit more detail on my blog. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…8qh7 - yes, too bad he died at 33. Who knows what he might have done? He'd at least have enjoyed the discovery of the electron in 1897. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…syfp - I haven't seen that. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…sz8l - Maybe: it's hard for me to be sure. He's talking about changes in curvature. What sort of continuity equation applies to curvature? Did he know about the Bianchi identities? Was he just spitballing? Or did mean something else, like the curvature should be a continuous function? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez Amazing steampunk mission to see whether space is curved... almost thwarted by a shipwreck, but our hero was not so easily stopped. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g3ts - I think Gauss studied surveyor's measurements. But maybe he suggested using astronomical observations too. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…8sqd - thanks! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…sz8l - I've never even tried to read that one! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…lx54 - is the decay of Higgs into a charmed quark (and some other stuff) a process we should expect to see with current equipment? npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…sz8l @nprofile…8qh7 - yes, in science you have to really love the work for its own sake, not for any glory it might bring, because even if you come up with an important idea there's a good chance you'll be largey ignored and someone else will get the glory. You will still have the joy of discovery. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…t6k2 - yes, it's an instance of that. Poincare in particular was too sophisticated for his own good, correctly arguing that different conceptual frameworks were possible for explaining the phenomena of relativistic time dilation, length contraction, etc., while Einstein strongly argued for *one* framework, in retrospect the best one - and then took advantage of this to revolutionize physics. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…8qh7 - pretty funny. You know things aren't so bad when items like that get to make the news. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…2c7j - I'll point this out to @nprofile…97ud. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…yhyk @nprofile…hmdu - yes, you can't really describe a particle falling through a viscous fluid using a time-independent Lagrangian unless do something like model the fluid has having lots of tiny parts that get affected as the particle falls through the fluid. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…fh5j - I think the bishop was against all proposed laws saying God *had* to do this, that or the other thing. But if God *wants* to be affected by our prayers, that's fine. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…ldmj - I think the Principle of Reciprocity is more general than conservation of momentum in systems with a translation-invariant Lagrangian. In Lagrangian mechanics whenever the value of one quantity affects another, the other affects the one. Ultimately I feel it must boil down to the equality of mixed partial derivatives, ∂²𝑓/∂𝑥∂𝑦 = ∂²𝑓/∂𝑦∂𝑥. However I have never worked out the details so I may be wrong! I should get to the bottom of this. I can probably do it. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…vhdw - great! I think my talks and Humphrey's books are at opposite ends of a stylistic spectrum so they should complement each other. I've gotten a lot out of his book, btw! npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…vhdw - Okay! Dynkin diagrams are used for many things, so even if you know why you want to understand them, you might not know *all* the reasons you should want to understand them. My goal was go through those rather efficiently, skipping all hard proofs. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…g0zc - at last I know what you look like. npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6m John Carlos Baez @nprofile…7z30 - well do I know that view!
